Question

a bag contains 56 marbles. each marble is either red, green, or yellow. a marble is randomly removed from the bag and then returned to the bag. the probability that this marble is red is 5/8. the probability that this marble is green is 1/7. how many yellow marbles are in the bag?

Answer 1

1/7 + 5/8 + x = 56
43/56 + x = 56
13 = x

Answer 2

The first time I solved this problem, I did it in a way that I had to
mess with changing fractions to common denominators and all that.
Suddenly, however, the clean and easy way to do it dawned on me.
Here it is:

-- There are 56 marble in the bag.

-- The probability of pulling a red marble is 5/8, so
5/8 of the 56 marbles must be red.
5/8 of 56 = 35 red marbles.

-- The probability of pulling a green marble is 1/7,
so 1/7 of the 56 marbles must be green.
1/7 of 56 = 8 green marbles.

-- The red and green marbles make up (35 + 8) = 43
of the 56 marbles in the bag.

-- The rest of them are yellow.
There are (56 - 43) = 13 yellow marbles in the bag.

-- The probability of pulling a yellow marble is 13/56 . (about 23.2%)

No messy fractions at all !
That's the way I like it !